Nonlinear Integrals and Their Applications in Data Mining

Nonlinear Integrals and Their Applications in Data Mining

Author: Zhenyuan Wang

Publisher: World Scientific

Published: 2010

Total Pages: 359

ISBN-13: 9812814671

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Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area.


Book Synopsis Nonlinear Integrals and Their Applications in Data Mining by : Zhenyuan Wang

Download or read book Nonlinear Integrals and Their Applications in Data Mining written by Zhenyuan Wang and published by World Scientific. This book was released on 2010 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area.

Nonlinear Integrals and Their Applications in Data Mining

Nonlinear Integrals and Their Applications in Data Mining

Author: Zhenyuan Wang

Publisher: World Scientific

Published: 2010

Total Pages: 359

ISBN-13: 981281468X

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Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII


Book Synopsis Nonlinear Integrals and Their Applications in Data Mining by : Zhenyuan Wang

Download or read book Nonlinear Integrals and Their Applications in Data Mining written by Zhenyuan Wang and published by World Scientific. This book was released on 2010 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII

Optimization Based Data Mining: Theory and Applications

Optimization Based Data Mining: Theory and Applications

Author: Yong Shi

Publisher: Springer Science & Business Media

Published: 2011-05-16

Total Pages: 314

ISBN-13: 0857295047

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Optimization techniques have been widely adopted to implement various data mining algorithms. In addition to well-known Support Vector Machines (SVMs) (which are based on quadratic programming), different versions of Multiple Criteria Programming (MCP) have been extensively used in data separations. Since optimization based data mining methods differ from statistics, decision tree induction, and neural networks, their theoretical inspiration has attracted many researchers who are interested in algorithm development of data mining. Optimization based Data Mining: Theory and Applications, mainly focuses on MCP and SVM especially their recent theoretical progress and real-life applications in various fields. These include finance, web services, bio-informatics and petroleum engineering, which has triggered the interest of practitioners who look for new methods to improve the results of data mining for knowledge discovery. Most of the material in this book is directly from the research and application activities that the authors’ research group has conducted over the last ten years. Aimed at practitioners and graduates who have a fundamental knowledge in data mining, it demonstrates the basic concepts and foundations on how to use optimization techniques to deal with data mining problems.


Book Synopsis Optimization Based Data Mining: Theory and Applications by : Yong Shi

Download or read book Optimization Based Data Mining: Theory and Applications written by Yong Shi and published by Springer Science & Business Media. This book was released on 2011-05-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization techniques have been widely adopted to implement various data mining algorithms. In addition to well-known Support Vector Machines (SVMs) (which are based on quadratic programming), different versions of Multiple Criteria Programming (MCP) have been extensively used in data separations. Since optimization based data mining methods differ from statistics, decision tree induction, and neural networks, their theoretical inspiration has attracted many researchers who are interested in algorithm development of data mining. Optimization based Data Mining: Theory and Applications, mainly focuses on MCP and SVM especially their recent theoretical progress and real-life applications in various fields. These include finance, web services, bio-informatics and petroleum engineering, which has triggered the interest of practitioners who look for new methods to improve the results of data mining for knowledge discovery. Most of the material in this book is directly from the research and application activities that the authors’ research group has conducted over the last ten years. Aimed at practitioners and graduates who have a fundamental knowledge in data mining, it demonstrates the basic concepts and foundations on how to use optimization techniques to deal with data mining problems.

ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol II

ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol II

Author: Suresh Chandra Satapathy

Publisher: Springer Science & Business Media

Published: 2013-10-19

Total Pages: 780

ISBN-13: 3319030957

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This volume contains 85 papers presented at CSI 2013: 48th Annual Convention of Computer Society of India with the theme “ICT and Critical Infrastructure”. The convention was held during 13th –15th December 2013 at Hotel Novotel Varun Beach, Visakhapatnam and hosted by Computer Society of India, Vishakhapatnam Chapter in association with Vishakhapatnam Steel Plant, the flagship company of RINL, India. This volume contains papers mainly focused on Data Mining, Data Engineering and Image Processing, Software Engineering and Bio-Informatics, Network Security, Digital Forensics and Cyber Crime, Internet and Multimedia Applications and E-Governance Applications.


Book Synopsis ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol II by : Suresh Chandra Satapathy

Download or read book ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol II written by Suresh Chandra Satapathy and published by Springer Science & Business Media. This book was released on 2013-10-19 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 85 papers presented at CSI 2013: 48th Annual Convention of Computer Society of India with the theme “ICT and Critical Infrastructure”. The convention was held during 13th –15th December 2013 at Hotel Novotel Varun Beach, Visakhapatnam and hosted by Computer Society of India, Vishakhapatnam Chapter in association with Vishakhapatnam Steel Plant, the flagship company of RINL, India. This volume contains papers mainly focused on Data Mining, Data Engineering and Image Processing, Software Engineering and Bio-Informatics, Network Security, Digital Forensics and Cyber Crime, Internet and Multimedia Applications and E-Governance Applications.

The Journal of Fuzzy Mathematics

The Journal of Fuzzy Mathematics

Author:

Publisher:

Published: 2000

Total Pages: 548

ISBN-13:

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Book Synopsis The Journal of Fuzzy Mathematics by :

Download or read book The Journal of Fuzzy Mathematics written by and published by . This book was released on 2000 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Data Mining Applications for Empowering Knowledge Societies

Data Mining Applications for Empowering Knowledge Societies

Author: Hakikur Rahman

Publisher: IGI Global Snippet

Published: 2009

Total Pages: 368

ISBN-13:

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"This book presents an overview on the main issues of data mining, including its classification, regression, clustering, and ethical issues"--Provided by publisher.


Book Synopsis Data Mining Applications for Empowering Knowledge Societies by : Hakikur Rahman

Download or read book Data Mining Applications for Empowering Knowledge Societies written by Hakikur Rahman and published by IGI Global Snippet. This book was released on 2009 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents an overview on the main issues of data mining, including its classification, regression, clustering, and ethical issues"--Provided by publisher.

Advances in Heat Transfer

Advances in Heat Transfer

Author:

Publisher: Academic Press

Published: 1998-05-18

Total Pages: 467

ISBN-13: 0080575846

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Advances in Heat Transfer


Book Synopsis Advances in Heat Transfer by :

Download or read book Advances in Heat Transfer written by and published by Academic Press. This book was released on 1998-05-18 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Heat Transfer

Dissertation Abstracts International

Dissertation Abstracts International

Author:

Publisher:

Published: 2008

Total Pages: 994

ISBN-13:

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Book Synopsis Dissertation Abstracts International by :

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Functional Analysis and Applications

Nonlinear Functional Analysis and Applications

Author: Louis B. Rall

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 595

ISBN-13: 1483272443

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Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.


Book Synopsis Nonlinear Functional Analysis and Applications by : Louis B. Rall

Download or read book Nonlinear Functional Analysis and Applications written by Louis B. Rall and published by Elsevier. This book was released on 2014-05-10 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.

Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects

Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects

Author: Petra Perner

Publisher: Springer

Published: 2008-07-14

Total Pages: 454

ISBN-13: 3540707204

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ICDM / MLDM Medaillie (limited edition) Meissner Porcellan, the “White Gold” of King August the Strongest of Saxonia ICDM 2008 was the eighth event of the Industrial Conference on Data Mining held in Leipzig (www.data-mining-forum.de). For this edition the Program Committee received 116 submissions from 20 countries. After the peer-review process, we accepted 36 high-quality papers for oral presentation, which are included in these proceedings. The topics range from aspects of classification and prediction, clustering, Web mining, data mining in medicine, applications of data mining, time series and frequent pattern mining, and association rule mining. Thirteen papers were selected for poster presentations that are published in the ICDM Poster Proceeding Volume. In conjunction with ICDM there were three workshops focusing on special hot application-oriented topics in data mining. The workshop Data Mining in Life Science DMLS 2008 was held the third time this year and the workshop Data Mining in Marketing DMM 2008 ran for the second time this year. Additionally, we introduced an International Workshop on Case-Based Reasoning for Multimedia Data CBR-MD.


Book Synopsis Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects by : Petra Perner

Download or read book Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects written by Petra Perner and published by Springer. This book was released on 2008-07-14 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICDM / MLDM Medaillie (limited edition) Meissner Porcellan, the “White Gold” of King August the Strongest of Saxonia ICDM 2008 was the eighth event of the Industrial Conference on Data Mining held in Leipzig (www.data-mining-forum.de). For this edition the Program Committee received 116 submissions from 20 countries. After the peer-review process, we accepted 36 high-quality papers for oral presentation, which are included in these proceedings. The topics range from aspects of classification and prediction, clustering, Web mining, data mining in medicine, applications of data mining, time series and frequent pattern mining, and association rule mining. Thirteen papers were selected for poster presentations that are published in the ICDM Poster Proceeding Volume. In conjunction with ICDM there were three workshops focusing on special hot application-oriented topics in data mining. The workshop Data Mining in Life Science DMLS 2008 was held the third time this year and the workshop Data Mining in Marketing DMM 2008 ran for the second time this year. Additionally, we introduced an International Workshop on Case-Based Reasoning for Multimedia Data CBR-MD.